Maths education for innovative societies

by Stéphan Vincent-Lancrin
Senior Analyst and Project Leader, Directorate for Education and Skills

Mathematics is at the core of science, engineering and technology. Mathematic modelling of various phenomena underpins technology innovation. No wonder that mathematics education has always ranked high on the innovation policy agenda.

There is now ample evidence that preparing students for an innovative society goes well beyond preparing them for science-related professions. Given that a large share of professionals contributes in some way to innovation, the new educational imperative is to equip a critical mass of workers and citizens with the skills to thrive in innovative societies.

How can education systems meet this demand through mathematics education? First, they should improve students’ technical skills in mathematics. By technical skills, I mean the know-what (for example, the theorems) and the know-how (for example, the procedures to solve different types of problems). The 2012 results of the OECD Programme for International Student Assessment (PISA) show that many countries still have room for improvement. They also reveal that too many students still perceive mathematics as an educational stumbling block.

How could one possibly improve the learning outcomes in mathematics that are traditionally tested and, at the same time, develop other important skills for innovation, such as reasoning, understanding, posing (rather than just solving) problems, self-confidence, and even communication skills?

This is precisely the question that Zemira Mevarech and Bracha Kramarski address in a new OECD report entitled Critical Maths for Innovative Societies. Strong experimental and quasi-experimental research evidence points to one solution that teachers could easily adopt more systematically in their teaching: the explicit teaching of metacognitive strategies.

Meta-what? Let’s not be intimidated by scientific language. Metacognition simply means “thinking about” or “regulating” one’s thinking. While one often thinks about one’s thinking when learning, metacognitive pedagogies make students develop explicit (rather than implicit) learning and problem-solving strategies by making them systematically go through a series of questions about their learning.

Initiated by the Hungarian mathematician George Polya, these strategies have had several developers and promoters. For example, the teaching method developed by Mevarech and Kramarski, called IMPROVE, asks students to answer four types of questions when exposed to new content knowledge or when solving a problem: comprehension questions (e.g. what is the problem about?); connection questions (e.g. how does this problem relate to problems I have already solved? Please explain your reasoning); strategic questions (e.g. what kinds of strategies are appropriate for solving the problem, and why? Please explain your reasoning), and reflection questions (e.g. does the solution make sense? can the problem be solved in a different way?). These questions and their related processes then gradually become a habit of mind. Rigorous research shows that using this pedagogy, and others like it,  yields positive results on a variety of outcomes and skills that matter in innovative societies.

First, compared to traditional pedagogies, these methods lead to better learning outcomes in arithmetic, algebra and geometry, and their effectiveness increases in co-operative learning settings and when they also address learners’ emotional responses.

Second, they do not enhance only traditional learning outcomes, but also other skills for innovation. Metacognitive pedagogies help students to articulate their thinking, actively use the “mathematics language”, be more curious as they relate their learning to their interests, provide elaborated explanations, and also be involved in conflict resolutions and mutual learning. Students thus become better at mathematical reasoning, and better at regulating their emotions when confronted with mathematical problems. Students who have been taught using these pedagogies show less anxiety towards mathematics, for example.

Metacognitive pedagogies work for students in primary, secondary and tertiary education, as well as in teacher training; and some longitudinal studies show that they have a lasting effect and lead to much better retention of knowledge.

A noteworthy finding for policy makers is that metacognitive strategies are effective both for traditional and for complex, unfamiliar and non-routine math problems. Because they can be more authentic, more open, and more related to real life, these kinds of problems may arguably better prepare students to exert their creative and critical minds. An example of such a problem is the following: “several supermarkets advertised that they are the cheapest supermarket in town. Please collect information and find out which of the advertisements is correct.” Students then have to design and implement a strategy to come up with a reasoned answer. These kinds of problems may have several solutions, depending on how students interpret the problem: the students may go for a different basket of goods, or take into account qualitative differences in a different way – as we do in real life.

Some mathematics educators believe that complex, unfamiliar and non-routine problems are not “real maths” problems; but the good news is that, whatever the type of problem they prefer, metacognitive strategies will still improve their students’ learning outcomes.

Would metacognitive pedagogies have positive effects if mainstreamed in mathematics education (and possibly other disciplines)? Singapore is the only country where metacognitive strategies are now one explicit dimension of the mathematics curriculum. That means they are taught in teacher training and teachers are obliged to use them. This might partly explain why Singapore is consistently one of the top performers in mathematics, in both the PISA and the Trends in International Mathematics and Science Study (TIMSS) tests.

Many educators and policy makers call for more evidence to support improvement of educational practices and reform education systems before adopting education reforms. For once, we have strong evidence. So why wait any longer to promote the use of metacognitive pedagogies in the classroom?

Links:
Critical Maths for Innovative Societies The Role of Metacognitive Pedagogies
PISA 2012 Results: Creative Problem Solving (Volume V)
PISA 2012 Results: What Students Know and Can Do (Volume I)
Measuring Innovation in Education: A New Perspective
Art for Art’s Sake? The Impact of Arts Education
The Nature of Learning: Using Research to Inspire Practice 
Centre for Educational Research and Innovation (CERI)
OECD Insights: Want to improve your problem solving skills? Try metacognition
Photo credit: © Aakash Nihalani (“Sum Times”)

How much do teachers cost?

by Eric Charbonnier and Etienne Albiser
Analysts, Directorate for Education and Skills

Can increasing the salaries of teachers lead to better learning outcomes? Does reducing class size have a positive effect on learning outcomes? Given the current background of tight public budgets, governments seeking to ensure value for money must ask themselves these questions before increasing the salary cost of teacher per student, as teachers account for a major part of education expenditure.

The latest edition of Education Indicators in Focus highlights that the salary cost of teacher per student is a combination of four factors: teachers’ salary, class size, the number of teaching hours in front of a classroom and the number of hours of instruction received by students.

Countries that have similar levels of expenditure on education do not necessarily have similar educational policies and practices. A given level of expenditure may result from a different combination of these factors. One country may pay higher salaries to teachers while another may have smaller class sizes and thus more teachers to pay.

Between 2000 and 2010, increases in the salary cost of teacher per student were mainly influenced by changes in teachers’ salaries and class size
 With the exception of France and Italy, the salary cost of teacher per student at the primary and lower secondary levels increased between 2000 and 2010, and on average it increased by one-third and one-quarter, respectively (for countries for which data is available). In the majority of cases, this increase was due to an increase in the level of teacher compensation (16% at the primary level and 14% at the lower secondary level). The largest salary increases (more than 50%, in constant prices) were seen in the Czech Republic, Estonia and Turkey.

During the same period, class size decreased, by 14% (primary) and 7% (lower secondary), but this was often the result of changing demographics and not of a change in education policies.

Little change in instruction time and teaching time
With the exception of a few countries, there was little or no change with respect to the two other variables (instruction time and teaching time) during the same period. This may be due to the political sensitivity of reforms in these areas. At the primary level, teaching time increased most significantly in the Czech Republic (200 hours) and instruction time increased the most in Iceland (by nearly 200 hours).

The higher the level of education, the higher the salary cost of teacher per student, with great disparities between countries
Spending on education rises sharply with the level of education. The OECD average salary cost of teachers is USD 2 307 per primary student, USD 2 856 per lower secondary student and USD 3 301 per upper secondary student. In some countries, the differences between the different levels of education is quite small (in Chile and Hungary it is less than USD 50) while in others it is quite important (exceeding USD 2 000 in the Flemish Community in Belgium).

In general, teachers of higher levels of education earn more money than teachers at lower levels. In addition, teaching time generally decrease as the level of education increases (meaning that more teachers are necessary to teach the same number of students).

Wrapping up
Reforms relating to these four factors have an impact on education expenditure and may also affect learning outcomes. However, the link between expenditure and outcomes is not straightforward. PISA results show that between 2000-2009, the performance of 15-years olds did not vary significantly in the majority of countries, regardless of the changes we have seen in instruction time, teaching time, class size and teacher compensation. What is more, changes relating to pedagogy may have an impact on outcomes without necessarily having an impact on expenditure.

The bottom line is that in the past ten years, increasing teachers’ salaries and reducing class size have not led to better learning outcomes in the majority of countries. This raises the question: has all of the additional money been well spent?

For more information
On this topic, visit:
Education Indicators in Focus: www.oecd.org/education/indicators
On the OECD’s education indicators, visit:
Education at a Glance 2012: OECD Indicators: www.oecd.org/edu/eag2012
Chart source: OECD Education at a Glance 2012:  Indicator B7 (www.oecd.org/edu/eag2012)

A Window into the classroom

Dirk Van Damme
by Division Head, Innovation and Measuring Progress (IMEP) and Head of Centre for Educational Research and Innovation (CERI)

An excellent teacher is what makes students learn and succeed in school. Everything else – standards, curricula, assessments, resources, school leadership – come second. Yet, what do we actually know about what teachers are doing?

Classrooms seem to be the ‘black boxes’ of the education system. There is not an awful lot of research on classroom teaching practices, but TALIS 2008 provides some self-reported data on teaching practices and professional activities including participation in collaborative learning with colleagues. The main TALIS report, published in 2009, compared the relative preference for three different teaching practices – structuring, student oriented and enhanced activities – across the 23 different countries that participated in the survey. The report showed differences between countries regarding the extent to which teachers are favouring directive and teacher-directed practices over more activating and learner-centred ones. These TALIS results were received as rather disappointing signals, suggesting that the teaching profession was relatively resistant to change in many countries.

In collaboration with the TALIS programme and as part of its Innovative Teaching for Effective Learning project the OECD’s Centre for Educational Research and Innovation (CERI) has just released a research report which delves deeper in the TALIS data on teaching practices in classrooms and schools. Based on some advanced analytical tools (multilevel latent profile analysis), this new book called Teaching Practices and Pedagogical Innovations: Evidence from TALIS  identifies underlying profiles in teachers’ classroom practices. A large set of variables about teachers, such as gender, training, subjects taught, but also their pedagogical beliefs, the degree of professional development, the amount of feedback and appraisal received, etc., were brought together and in each country different profiles of teachers were distinguished.

The scientific and policy implications of this research are huge. Many learning researchers and education policy makers strongly – and rightly so – believe in the benefits of more student-oriented, self-regulating approaches to teaching and learning. This suggests that a particular form of teaching is outdated and should be replaced by a more innovative one. Consequently, this report now suggests that we should not look at the quality of what happens in classrooms in an ‘either-or’ way. While it is true that the best teachers differ from their colleagues in their relative use of activating, student-oriented ways of teaching, they also use more structuring, teacher-driven forms of classroom practice. Teaching quality is a matter of diversity of practices, not of one set of practices against the other. Excellent teachers are those teachers who master a large repertoire of teaching practices, which they can deploy according to learners’ needs and varying classroom conditions. Those teachers are also the ones who actively advance their own professional competence by professional development and who feel more satisfied and effective about their own work.

A final important finding is that there is also a clear difference between these teacher profiles in the degree of co-operation with other colleagues and engagement in collaborative learning communities in and outside schools. Excellent teachers view teaching as a collective responsibility within the profession, not as an individualised thing happening behind closed doors. They open the doors of their classrooms, inviting colleagues to engage in what they are doing but also disclosing what happens in classrooms to the outside world. It is that kind of teachers we need to work with our kids.

Links:
Centre for Educational Research and Innovation (CERI) Activities
OECD Teaching and Learning International Survey (TALIS)
Teaching in Focus Briefs

Photo credit: © By happy via